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Statistical analysis of outer large-scale/inner-layer interactions in channel flow subjected to oscillatory drag-reducing wall motion using a multiple-variable joint-probability-density function methodology

Published online by Cambridge University Press:  27 July 2021

Lionel Agostini Open the ORCID record for Lionel Agostini [Opens in a new window]  and
Michael Leschziner Open the ORCID record for Michael Leschziner [Opens in a new window]
Lionel Agostini*
Affiliation:
Institut Pprime, CNRS / Université de Poitiers / ENSMA, Poitiers86073, France
Michael Leschziner
Affiliation:
Department of Aeronautics, Imperial College London, LondonSW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

Full flow-field data derived from a direct numerical simulation for channel flow subjected to drag-reducing oscillatory spanwise motion are analysed by means of a recently developed methodology, which consolidates the entire simulation data set within multiple-variable joint-probability-density functions (PDFs). A wide variety of statistical data of interest are then extracted from the joint PDF without recourse to any of the original simulation data. The nominal friction Reynolds number of the baseline (unactuated) flow is 1025, and the actuation is effected at a wall-scaled period of 100, at which value the drag-reduction level is approximately 30 %, while any actuation-induced phase fluctuations in the streamwise direction are minimal. Interest focuses on the elucidation of the mechanisms by which the near-wall turbulence is modified by the action of footprints of large-scale structures in the outer parts of the log-law region, which tend to intensify as the Reynolds number rises. To elucidate these mechanisms, the Reynolds stresses and their production rates, conditional on the intensity of large-scale skin-friction fluctuations, are examined. The investigation includes a separation of the Reynolds stresses into large-scale and small-scale components by means the empirical mode decomposition, allowing the intensity of footprinting and of small-scale modulation of the near-wall turbulence to be quantified separately. The conditional statistical properties are presented in the form of maps in planes having the wall-normal distance and large-scale skin friction as coordinates, supplemented by wall-normal property profiles and an examination of large-scale and small-scale contributions to the skin friction. The analysis highlights the strongly asymmetric response of the production rate and the turbulence level in the buffer layer to positive vs. negative footprints, the former strongly enhancing small-scale turbulence. This is proposed to be at least a partial explanation of the decline in the drag-reduction effectiveness of oscillatory spanwise wall motion with increasing Reynolds number.

JFM classification

Boundary Layers: Boundary layer control Flow Control: Drag reduction
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 923 , 25 September 2021 , A25
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Abdulbari, H.A, Yunus, R.M., Abdurahman, N.H. & Charles, A. 2013 Going against the flow–a review of non-additive means of drag reduction. J. Indus. Engng Chem. 19 (1), 27–36.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M.A. 2014 On the influence of outer large-scale structures on near-wall turbulence in channel flow. Phys. Fluids 26 (7), 075107.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M.A. 2016 Predicting the response of small-scale near-wall turbulence to large-scale outer motions. Phys. Fluids 28 (1), 015107.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M.A. 2017 Spectral analysis of near-wall turbulence in channel flow at ${Re}_{\tau }=4200$ with emphasis on the attached-eddy hypothesis. Phys. Rev. Fluids 2, 014603.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M.A. 2018 The impact of footprints of large-scale outer structures on the near-wall layer in the presence of drag-reducing spanwise wall motion. Flow Turbul. Combust. 100, 1037–1061.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M.A. 2019 a The connection between the spectrum of turbulent scales and the skin-friction statistics in channel flow at $Re_\tau \approx 1000$. J. Fluid Mech. 871, 22–51.CrossRefGoogle Scholar
Agostini, L. & Leschziner, M.A. 2019 b On the departure of near-wall turbulence from the quasi-steady state. J. Fluid Mech. 871, R1.CrossRefGoogle Scholar
Agostini, L., Leschziner, M.A. & Gaitonde, D. 2016 Skewness-induced asymmetric modulation of small-scale turbulence by large-scale structures. Phys. Fluids 28 (1), 015110.CrossRefGoogle Scholar
Agostini, L., Leschziner, M.A., Poggie, J., Bisek, N.J. & Gaitonde, D. 2017 Multi-scale interactions in a compressible boundary layer. J. Turbul. 18 (8), 760–780.CrossRefGoogle Scholar
Agostini, L., Touber, E. & Leschziner, M.A. 2014 Spanwise oscillatory wall motion in channel flow: drag-reduction mechanisms inferred from DNS-predicted phase-wise property variations at ${Re}_{\tau }=1000$. J. Fluid Mech. 743, 606–635.CrossRefGoogle Scholar
Agostini, L, Touber, E & Leschziner, M.A. 2015 The turbulence vorticity as a window to the physics of friction-drag reduction by oscillatory wall motion. Intl J. Heat Fluid Flow 51, 3–15.CrossRefGoogle Scholar
Asidin, M.A., Suali, E, Jusnukin, T & Lahin, F.A. 2019 Review on the applications and developments of drag reducing polymer in turbulent pipe flow. Chinese J. Chem. Engng 27 (8), 1921–1932.CrossRefGoogle Scholar
Blesbois, O., Chernyshenko, S.I., Touber, E. & Leschziner, M.A. 2013 Pattern prediction by linear analysis of turbulent flow with drag reduction by wall oscillation. J. Fluid Mech. 724, 607–641.CrossRefGoogle Scholar
Choi, K.-S. 2000 European drag-reduction research – recent developments and current status. Fluid Dyn. Res. 26 (5), 325.CrossRefGoogle Scholar
Choi, K.-S., Jukes, T. & Whalley, R. 2011 Turbulent boundary-layer control with plasma actuators. Phil. Trans. R. Soc. A: Math. Phys. Engng Sci. 369 (1940), 1443–1458.CrossRefGoogle ScholarPubMed
Corke, T.C & Thomas, F.O 2020 Method and apparatus of plasma flow control for drag reduction. US Patent 10527074.Google Scholar
Del Álamo, J.C & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41.CrossRefGoogle Scholar
Du, Y. & Karniadakis, G.E. 2000 Suppressing wall turbulence by means of a transverse traveling wave. Science 288 (5469), 1230–1234.CrossRefGoogle ScholarPubMed
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14 (11), L73–L76.CrossRefGoogle Scholar
Gatti, D. & Quadrio, M. 2013 Performance losses of drag-reducing spanwise forcing at moderate values of the Reynolds number. Phys. Fluids 25 (12), 125109.CrossRefGoogle Scholar
Gatti, D. & Quadrio, M. 2016 Reynolds-number dependence of turbulent skin-friction drag reduction induced by spanwise forcing. J. Fluid Mech. 802, 553–582.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to $Re= 2003$. Phys. Fluids 18, 011702.CrossRefGoogle Scholar
Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N. -C., Tung, C.C. & Liu, H.H. 1998 The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. Ser. A: Math. Phys. Engng Sci. 454 (1971), 903–995.CrossRefGoogle Scholar
Hurst, E., Yang, Q. & Chung, Y.M 2014 The effect of reynolds number on turbulent drag reduction by streamwise travelling waves. J. Fluid Mech. 759, 28–55.CrossRefGoogle Scholar
Hutchins, N, Nickels, T.B, Marusic, I & Chong, M.S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103–136.CrossRefGoogle Scholar
Karniadakis, G.E. & Choi, K.S. 2003 Mechanisms on transverse motions in turbulent wall flows. Annu. Rev. Fluid Mech. 35 (1), 45–62.CrossRefGoogle Scholar
Leschziner, M.A. 2020 Friction-drag reduction by transverse wall motion – a review. J. Mech. 36 (5), 649–663.CrossRefGoogle Scholar
Lozano-Durán, A, Bae, H.J & Encinar, M.P. 2020 Causality of energy-containing eddies in wall turbulence. J. Fluid Mech. 882, A2.CrossRefGoogle Scholar
Marusic, I. & Heuer, W.D.C. 2007 Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99 (11), 114504.CrossRefGoogle ScholarPubMed
Marusic, I., Mathis, R. & Hutchins, N. 2010 High Reynolds number effects in wall turbulence. Intl J. Heat Fluid Flow 31 (3), 418–428.CrossRefGoogle Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.CrossRefGoogle Scholar
Örlü, R., Fiorini, T., Segalini, A., Bellani, G., Talamelli, A. & Alfredsson, P.H. 2017 Reynolds stress scaling in pipe flow turbulence – first results from ciclope. Phil. Trans. R. Soc. Lond. A: Math. Phys. Engng Sci. 375 (2089), 20160187.Google ScholarPubMed
Quadrio, M. 2011 Drag reduction in turbulent boundary layers by in-plane wall motion. Phil. Trans. R. Soc. A: Math. Phys. Engng Sci. 369 (1940), 1428–1442.CrossRefGoogle ScholarPubMed
Quadrio, M., Ricco, P. & Viotti, C. 2009 Streamwise-travelling waves of spanwise wall velocity for turbulent drag reduction. J. Fluid Mech. 627, 161–178.CrossRefGoogle Scholar
Ricco, P., Ottonelli, C., Hasegawa, Y. & Quadrio, M. 2012 Changes in turbulent dissipation in a channel flow with oscillating walls. J. Fluid Mech. 700 (1), 1–28.CrossRefGoogle Scholar
Ricco, P., Skote, M. & Leschziner, M.A. 2021 A review of turbulent skin-friction drag reduction by near-wall transverse forcing. Prog. Aerosp. Sci. 123, 100713.CrossRefGoogle Scholar
Smits, A.J, McKeon, B.J & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.CrossRefGoogle Scholar
Touber, E. & Leschziner, M.A. 2012 Near-wall streak modification by spanwise oscillatory wall motion and drag-reduction mechanisms. J. Fluid Mech. 693, 150–200.CrossRefGoogle Scholar
Wong, C.W., Zhou, Y., Li, Y.Z. & Li, Y.P. 2015 Active drag reduction in a turbulent boundary layer based on plasma-actuator-generated streamwise vortices. In Proceedings of the 9th International Symposium on Turbulence and Shear Flow Phenomena.Google Scholar
Yao, J., Chen, X. & Hussain, F. 2018 Drag control in wall-bounded turbulent flows via spanwise opposed wall-jet forcing. J. Fluid Mech. 852, 678–709.CrossRefGoogle Scholar
Yao, J., Chen, X., Thomas, F. & Hussain, F. 2017 Large-scale control strategy for drag reduction in turbulent channel flows. Phys. Rev. Fluids 2 (6), 062601.CrossRefGoogle Scholar
Zhang, L., Shan, X. & Xie, T. 2020 Active control for wall drag reduction: methods, mechanisms and performance. IEEE Access 8, 7039–7057.CrossRefGoogle Scholar